T7 Phage Display

I am using the T7 Phage display system to find high affinity binders. My bait protein (140kDa) is His-tagged. I have incubated the phage with the bait protein and then incubated this with Nickel resin to pull out the binding phage.

At the end of the first round I see a 3-fold difference between with and no bait, 300000pfu/ml and 90000pfu/ml respectively.

For the second round I slight decreased the incubation time (30mins to 20mins) and increased the number of washes (5 to 8 1ml washes) and see a 5-fold difference 100000pfu/ml and 20000pfu/ml for bait and no bait respectively.

On the third round I repeated the second round method but see around 30000pfu/ml for both bait and no bait.

I am using imidazole to elute the phage by releasing the bait protein.

My question concerns if the bait protein is interfering with phage replication so that the background phage overtake the positive binding phage and whether I should use a different method to disrupt the protein-protein interaction?
I can not use ELISA plates as the bait protein contains an intrinsically disordered domain and binding to the ELISA prevents phage binding.